Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras

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Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras. / Ivanov, Sergei O.; Lopatkin, Viktor.

в: Journal of Pure and Applied Algebra, Том 225, № 11, 106725, 11.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{6f16b46b6b27412489317b72320181fe,

title = "Parafree augmented algebras and Gr{\"o}bner-Shirshov bases for complete augmented algebras",

abstract = "We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of a finitely generated parafree augmented algebra of infinite cohomological dimension. Motivated by this example, we prove a version of the Composition-Diamond lemma for complete augmented algebras and give a sufficient condition for an augmented algebra to be residually nilpotent in terms of its relations.",

keywords = "CD-lemma for power series, Gr{\"o}bner–Shirshov basis, Parafree augmented algebras, The parafree conjecture",

author = "Ivanov, {Sergei O.} and Viktor Lopatkin",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = nov,

doi = "10.1016/j.jpaa.2021.106725",

language = "English",

volume = "225",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

number = "11",

}

RIS

TY - JOUR

T1 - Parafree augmented algebras and Gröbner-Shirshov bases for complete augmented algebras

AU - Ivanov, Sergei O.

AU - Lopatkin, Viktor

PY - 2021/11

Y1 - 2021/11

N2 - We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of a finitely generated parafree augmented algebra of infinite cohomological dimension. Motivated by this example, we prove a version of the Composition-Diamond lemma for complete augmented algebras and give a sufficient condition for an augmented algebra to be residually nilpotent in terms of its relations.

AB - We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of a finitely generated parafree augmented algebra of infinite cohomological dimension. Motivated by this example, we prove a version of the Composition-Diamond lemma for complete augmented algebras and give a sufficient condition for an augmented algebra to be residually nilpotent in terms of its relations.

KW - CD-lemma for power series

KW - Gröbner–Shirshov basis

KW - Parafree augmented algebras

KW - The parafree conjecture

UR - http://www.scopus.com/inward/record.url?scp=85102893923&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2021.106725

DO - 10.1016/j.jpaa.2021.106725

M3 - Article

AN - SCOPUS:85102893923

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 11

M1 - 106725

ER -

ID: 90651077